The error states that the window can't be created. It might be the problem with parameters to the window creation function (that should not depend on game state), or maybe the system is out of memory. Resources allocated in memory are never cleaned up because cleanup time overflows?
Doom4CE (this port) was based on WinDoom, which only creates the program window once at startup, then switches the graphical mode, and proceeds to draw on screen independently, processing the keyboard and mouse input messages. I'm not sure, but maybe Windows CE memory management forced the programmer to drop everything and start from scratch at the load of each level? Then why do we see the old window?
There are various 32 bit integer counters in Doom code. I find it quite strange that the author neither names the specific one, nor what it does, nor tries to debug what happens by simply initialising it with some big value.
Moreover, 2^32 divided by 60 frames per second, then by 60 seconds, 60 minutes, 24 hours, 30 days, and 12 months gives us a little less than 2.5 years. However, Doom gameplay tick (or “tic”), on which everything else is based, famously happens only 35 times a second, and is detached from frame rendering rate on both systems that are too slow (many computers at the time of release), or too fast (most systems that appeared afterwards). 2^32 divided by 35, 60 seconds, etc. gives us about 4 years until overflow.
Would be hilarious if it really is such an easy mistake.